Device and method for the geometric determination of electrical dipole densities on the cardiac wall
Disclosed are devices, a systems, and methods for determining the dipole densities on heart walls. In particular, a triangularization of the heart wall is performed in which the dipole density of each of multiple regions correlate to the potential measured at various locations within the associated chamber of the heart.
1. A system for generating a database of dipole densities d(y) at the surface of one or more cardiac chambers of a patient, comprising:
an electrode array including multiple electrodes for insertion into a cardiac chamber of a patient;
at least one skin electrode;
a receiver configured to record mapping information from the electrode array and the at least one skin electrode; and
a dipole density module comprising computer logic executable by at least one processor to create a database of dipole densities d(y) at the surface of the cardiac chamber based on mapping information and a geometrical depiction of the cardiac chamber.
2. The system according to claim 1 , wherein the database of dipole densities d(y) includes dipole density information for individual triangle-shaped projections onto the surface of the cardiac chamber.
3. The system according to claim 2 , wherein the number of triangle-shaped projections is chosen such that the dipole density d(y) of each triangle-shaped projection is substantially constant.
4. The system according to claim 2 , wherein the number of triangle-shaped projections is at least 1,000.
5. The system according to claim 2 , wherein each triangle-shaped projection at a location y contributes {acute over (ω)}(x,y) times the dipole density d(y) to a potential V(x) at a point x, wherein {acute over (ω)}(x,y) is the solid angle for that triangle projection, and where:
a) x represents a series of locations within one or more cardiac chambers; and
b) V(x) is a measured potential at point x, said measured potential recorded by the multiple electrodes.
6. The system according to claim 1 , wherein the electrode array includes a three-dimensional array of electrodes.
7. The system according to claim 1 , wherein the dipole densities of the database d(y) of dipole densities are mapped to the one or more surfaces of the one or more cardiac chambers.
8. The system according to claim 7 , wherein the dipole density module is further configured to create two or more maps of the dipole densities d(y), and wherein each of the two or more maps are at different time intervals.
9. The system according to claim 8 , wherein the dipole density module is further configured to synthesize the at least two maps of dipole densities d(y) at different time intervals to create an activation sequence of cardiac activity over a plurality of time intervals.
10. The system according to claim 1 , wherein the dipole density module is further configured to update the database of dipole densities d(y) at a plurality of time intervals during cardiac activity.
11. The system according to claim 10 , wherein the plurality of time intervals includes at least one time interval per cardiac cycle.
12. The system according to claim 10 , wherein the plurality of time intervals includes a plurality of time intervals per cardiac cycle.
13. The system according to claim 10 , wherein the plurality of time intervals includes a time interval of about a millisecond.
14. The system according to claim 1 , wherein the multiple electrodes of the electrode array are included in a single catheter.
15. The system of claim 1 , wherein the dipole density module is configured to calculate and/or recalculate the dipole densities d(y) using the following equations:
W
k
=
∑
l
=
1
L
A
kl
V
l
.
(
1
)
wherein a small sinusoidal voltage V 1 is applied to each electrode l=1, . . . L on the electrode array in the heart, and the resulting voltages W k , k=1, . . . K is measured at the surface electrodes, which yields the K+L transition matrix A kl ;
V
l
=
∑
n
=
1
N
B
l
n
d
n
.
(
2
)
wherein calculating solid angles produces the linear transformation B ln between the electrode array potentials V 1 and the dipole densities d n ,n=1, . . . N of N regions of the cardiac chamber wall; and
W
k
=
∑
l
=
1
L
∑
n
=
1
N
A
kl
B
l
n
d
n
.
(
3
)
where equation (2) above is substituted into equation (1) to form equation (3).
16. The system according to claim 15 , wherein the dipole density module is configured to solve equations (2) and (3) using regularization techniques.
17. The system according to claim 16 , wherein the regularization techniques comprise Tikhonov regularization.
18. The system according to claim 1 , wherein the system is further configured to:
generate a computer display of dipole density information based on the database of dipole densities d(y); and
update the computer display of the dipole information based on updating the database of dipole densities d(y).
19. The system according to claim 1 , wherein the database of dipole densities d(y) represents a distribution and activity of dipole charge densities on one or more cardiac wall.
20. The system according to claim 1 , wherein the mapping information recorded from the at least one skin electrode is used to recalculate the database of dipole densities d(y).
21. The system according to claim 1 , wherein the at least one skin electrode comprises more than one skin electrode.
22. The system according to claim 1 , wherein the at least one skin electrode is configured for placement on a thorax.